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In this paper, a dimension reduction method via general orthogonal polynomials and multiorder Arnoldi algorithm is proposed, which focuses on the topic of structure-preserving for k-power bilinear systems. The main procedure is using a series of expansion coefficient vectors of each state variables in the space spanned by general orthogonal polynomials that satisfy a recurrence formula to generate a projection based on multiorder Arnoldi algorithm. The resulting reduced-order model not only matches a desired number of expansion coefficients of the original output but also retains the topology structure. Meanwhile, the stability is well preserved under some certain conditions and the error bound is also given. Finally, two numerical simulations are provided to illustrate the effectiveness of our proposed algorithm in the views of accuracy and computational cost. [ABSTRACT FROM AUTHOR]

This paper focuses on the resource allocation problem(RAP) with constraints under a fixed general directed topology by using the distributed sub-gradient algorithm with event-triggered scheme in multi-agent systems, where each agent owns a cost function and its state value is bounded. The distributed sub-gradient algorithm aims to minimise the total cost by a distributed manner while achieving an optimal solution. Unlike centralised methods, the triggering condition and algorithm for each agent are fully decentralised. At each instant of time, each agent updates its state by employing the states which are collected from itself and its neighbouring agents at their last triggering time. In order to illustrate the effectiveness of the proposed sub-gradient algorithm with event-triggered control law, one simulation example is presented before the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, a hierarchical PO-MOESP subspace identification algorithm for directed acyclic graphs (DAGs) is presented. The state of every node and the structure of the graph are assumed to be unknown. The method computes a hierarchical partition of the DAG by using projection matrices typically used in subspace identification methods applied in cascade. Then, the column space of the observability matrix of every node is sequentially estimated by projecting away the input-output data from the previous levels. A past input–output instrumental variable approach is adopted to deal with the noise. The topology of multilevel DAGs is revealed by dedicated projections applied on every level. Moreover, we provide a brief study of a more general class of DAGs that can be accurately represented by multilevel DAGs of reduced interconnection structure. Finally, three simulation examples are provided to show the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]